This paper explores the political involvement of transnational corporations and their directors in elaborating the project of 'climate capitalism' advanced to address climate change. Climate capitalism seeks to redirect investments from fossil energy to renewable energy generation, so as to foster an ecological modernization of production and reduce greenhouse gas (GHG) emissions. I use social network analysis to assess the potential for climate capitalism, as a project of a section of the corporate elite, to replace the current 'carboniferous capitalist' regime. Corporate-funded climate and environmental policy groups (CEPGs) constitute major venues for the corporate elite to assemble and plan their response to the climate crisis. By mapping out the network of board-level interlocks between CEPGs and the largest transnational corporations, I first find that certain CEPGs are centrally located among the global intercorporate network, and thus well positioned to promote climate capitalism among the corporate elite. Second, I delineate a climate capitalist inner circle that includes the individual members of the corporate community who arguably are able to exert the greatest power to shape climate capitalism. However, many of them, close to the oil and nuclear sectors, may support a long-term transition away from fossil fuels, incompatible with avoiding dangerous climatic warming.